Inhomogeneous plane waves are defined as waves with an exponential decrease of amplitude along a plane wavefront and are usually treated in ray theory as waves with complex-valued slowness and polarization vectors and complex rays. The inhomogeneous waves can also be treated in real ray theory, provided higher-order ray approximations are considered. In real ray theory, the ray expansion of the inhomogeneous waves consists of an infinite number of terms and may converge to an exact solution. The inhomogeneous P wave is linearly polarized in the zero-order ray approximation and propagates with the velocity of the homogeneous wave. Higher-order ray approximations modify and correct the kinematic as well as dynamic attributes of the zero-order ray solution. They produce a correct elliptical polarization of the P wave and cause the propagation velocity to be dependent on the wave inhomogeneity.
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